The horizontal power straps are half the width (or twice the pitch)
of vertical ones; metal resistivities are different; core power
consumption is 2W with 32 core Vdd and 32 core Vss pads; 30%
core is RAM blocked to metal-4; 20% is analog blocked to all layers.

Step 3 is to set out the values of
kan, kwn, kcn and mn
for each metal layer, and use these to calculate the value of L.

metal layer

1

2

3

4

5

6

kan

50%

100%

50%

100%

50%

200%

power metal allocated coefficient

kwn

80%

80%

80%

80%

80%

80%

power metal used coefficient

kcn

78%¹

100%

100%

100%

100%

350%²

conductivity coefficient

mn

50%

50%

50%

50%

20%

20%

core area blocked

¹78%=.07/.09; ²350%=.07/.02

The value of L depends on p which we don't know.
We iterate to the solution and use p=0 for the first estimate.

L =

kw1kc1(1-ps)(1-m1(1-ka2p)(1-ka3p))+

kw2kc2(1-m2(1-ka2p)(1-ka3p))+

kw3kc3(1-m3(1-ka2p)(1-ka3p))+

kw4kc4(1-m4(1-ka2p)(1-ka3p))+

kw5kc5(1-m5(1-ka2p)(1-ka3p))+

kw6kc6(1-m6(1-ka2p)(1-ka3p))

=

( 0.12 + 0.4 + 0.2 + 0.4 + 0.64 + 4.48 )

=

6.24

Step 4: Calculate the power strap allocation percentage p.
The solution must be iterated, and the calculation below shows the first iteration.

m1′ =

m1×(1-ka2p)(1-ka3p)

p =

{

Vddmin×Pnom

−kc1×ps(1-m1′)

}

×

1

(Vcore−Vmin)×Vdd2×G

L

=

{

1.164×2

−0.78×0.22×(1-0.5)

}

×

1

(1.155−1.08)×1.22×25

6.24

=

(0.860−0.086)×0.160 = 12.40%

As shown on the right, a spreadsheet can be used to iterate to the answer
of p=11.45%.

Step 5: Calculate the new core size.
If the initial core size estimate without power straps is x,
then with power straps the core size becomes x′

x′ =

x

=

x

= x+9.44%

√(((1−ka2p)(1−ka3p))

√(0.8855×0.9428)

The value 9.44% is called the IR Drop Adder.

The power strap widths are set by the user defined pitch,
strap allocation or width and the value of p
just calculated. An example is shown in the table below,
where we set the supply strap allocation to 5.5µm and compare
it to the old solution.

The new solution has allowed the vertical power strap pitch to go up from
one every 56µm to one every 96µm.
The core side is 646µm less and the core area is 13% less
than the first solution, due to double bonding of supply pads,
tighter Vddmin spec and wider metal-5 straps.